PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
90022^193091-123758127Yves Minet08/2012
90019*7^68780-258127Lelio R Paula09/2014
90032473^17130+17130^247358126Norbert Schneider10/2018
90042^193083-86968810558124Lelio R Paula10/2012
90052^193058-4558117Lelio R Paula04/2011
9006(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
900711^55795-4258105Lelio R Paula03/2013
90083^121779-1658104Lelio R Paula10/2012
9009(13*10^58103+191)/358104Robert Price08/2017
90102^192986+19558095Lelio R Paula04/2011
90117^68740+2*3^6874058093Mike Oakes07/2010
9012(85*10^58091-1)/358093Robert Price07/2017
9013(404*10^58087-53)/958089Robert Price11/2017
901412^53821+1158083Lelio R Paula02/2013
9015119^27979-11858072Norbert Schneider10/2013
9016(10223*2^192828+1)/24358049Lelio R Paula05/2014
90172^192808-112758041Yves Minet05/2013
9018(27*2^192803+1)/982758037Lelio R Paula07/2012
9019(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
90203*10^58032-2358033Robert Price11/2017
90212^192678+7294358002Enzo Doria04/2016
9022(13*10^57997-37)/357998Robert Price08/2017
90232^192657-318957996Yves Minet10/2014
90246^74525-14957992Lelio R Paula10/2012
902542^35723-4157988Norbert Schneider06/2014
9026(29*2^192625-1)/18357986Lelio R Paula01/2014
9027(3^121520-8)/384757977Lelio R Paula03/2012
9028(2^192596-5)/13957976Lelio R Paula02/2012
902910^57975+6783357976Patrick De Geest09/2013
903010^57975-4769357975Patrick De Geest09/2013
9031(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
903214025^13592+13592^1402557970Hans Havermann04/2019
9033(29*10^57967+673)/957968Robert Price10/2017
9034(3^121492-5)/457966Lelio R Paula03/2012
90352^192549+3557964Lelio R Paula04/2011
903628799!2+257962Robert Price10/2012
9037(7*2^192534-1)/134757957Lelio R Paula01/2014
90387001^15069-10057943Enzo Doria07/2012
9039L(277273)/1109092157940Donovan Johnson11/2005
9040(2^192469-1017)/3557938Lelio R Paula02/2012
90412^192457-1155*19245757936Henri Lifchitz02/2005
904212752^14111-14111^1275257934Norbert Schneider01/2019
90432^192443+138557932Lelio R Paula05/2011
9044132^27317-13157928Norbert Schneider03/2015
904541522!3-5904957912Robert Price12/2015
9046(3*2^192380-1)/16957911Lelio R Paula01/2014
90472^192339-251557900Yves Minet07/2014
90482^192303+769557889Lelio R Paula10/2012
90492^192273-595557880Lelio R Paula05/2011
90502^192257+1609557876Lelio R Paula05/2011
9051109^28401-257865Lelio R Paula10/2017
90522^192218-11186157864Enzo Doria05/2014
90532^192214-394157863Yves Minet04/2017
9054(2^192212+3)/25957860Lelio R Paula02/2012
9055(3^121270+8)/15593975357853Lelio R Paula03/2012
905680^30393-7957841Norbert Schneider03/2015
905720^44455-312357838Enzo Doria03/2013
90592^192122-19557835Lelio R Paula04/2011
9058(29*10^57834+91)/357835Robert Price03/2016
90608*6^74306+557823Lelio R Paula09/2014
9061(39^36341-1)/3857820Robert Price04/2012
90622^192037-11180557809Enzo Doria05/2014
90632^192023-192023^257805Henri Lifchitz05/2005
906421^43717+257804Ray Chandler08/2011
90658*5^82687+757797Lelio R Paula09/2014
906616459^3246+3246^1645957794Hans Havermann04/2019
90675^82680-2457791Lelio R Paula10/2012
9069(2^191915+47)/9557771Lelio R Paula02/2012
906812019^14160-14160^1201957771Norbert Schneider02/2019
9070(74*10^57763+133)/957764Robert Price10/2017
90716^74227-9557760Lelio R Paula10/2012
90722^191861+2983557756Lelio R Paula10/2012
90731908^17605+17605^190857755Serge Batalov05/2014
90745*10^57754+5957755Robert Price09/2016
9075(5*2^191821-1)/892406757738Lelio R Paula01/2014
907614100^12431+12431^1410057733Hans Havermann04/2019
90773*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
907841399!3-656157723Robert Price11/2015
9079(44*10^57721-233)/957722Robert Price10/2017
90802^191745+1757721Lelio R Paula04/2011
90812^191730-76157717Yves Minet01/2012
9082(2^191733-3)/225157715Lelio R Paula02/2012
90832^191698-11157707Lelio R Paula04/2011
9084(13*10^57691+23)/957692Robert Price02/2015
90852^191640-447557690Yves Minet03/2019
908620^44340-542357688Enzo Doria03/2013
9087(27*2^191629+1)/12557686Lelio R Paula07/2012
90884*10^57684+3*7^5768457685Mike Oakes11/2010
90892*3^120898+557684Lelio R Paula04/2014
9090(6883*2^191610-1)/734757681Lelio R Paula04/2015
90916^74117-4957675Lelio R Paula10/2012
90922^191586-11320157674Enzo Doria07/2014
90932^191580+19357672Lelio R Paula04/2011
9094(103*29^39433+10401)/457669Curtis Bright05/2015
90952^191560+25525557666Lelio R Paula05/2011
90962^191515-8557652Lelio R Paula04/2011
90972^191502-112757648Yves Minet05/2013
90982*5^82473-3^8247357647Mike Oakes08/2010
9099(13*10^57634-61)/357635Robert Price08/2017
910085^29868-29868^8557628Norbert Schneider11/2017
91012^191430+10357627Lelio R Paula04/2011
91023*2^191408+557621Lelio R Paula03/2014
91032^191382-185893157612Enzo Doria04/2016
91046*7^68163+557606Lelio R Paula09/2014
910591^29403-257602Lelio R Paula08/2013
910611^55308-795057598Enzo Doria02/2013
91072^191329+6557596Lelio R Paula04/2011
910811^55302-24057592Enzo Doria07/2012
91092^191299-103146757587Paul Bourdelais11/2012
91102^191295-11199157586Enzo Doria05/2014
91112^191279-129757581Yves Minet08/2012
911214827^7630+7630^1482757567Hans Havermann04/2019
91133*6^73961+557554Lelio R Paula09/2014
911416177^3610+3610^1617757550Hans Havermann04/2019
9115(3^120623+5)/5214457548Lelio R Paula04/2012
9116(17*10^57543-29)/357544Robert Price09/2017
911742^35445-4157537Norbert Schneider06/2014
9118(71^31079-1)/7057534Paul Bourdelais08/2017
91192^191069-72340357518Paul Bourdelais11/2012
91204*10^57506-357507Serge Batalov11/2010
912110^57501+6735957502Patrick De Geest06/2016
912210^57501-100000000157501Robert Price05/2016
912310^57501-24986157501Patrick De Geest06/2016
9124(9^60251+4^60251)/1357493Robert Price02/2013
912520^44184-600357485Enzo Doria03/2013
91262^190948+1270557482Lelio R Paula10/2012
91272^190945+2957481Henri Lifchitz06/2005
91282^190922-40157474Yves Minet01/2012
912915^48860+4657464Lelio R Paula02/2013
91303^120434+2057462Lelio R Paula10/2012
91317^67964-3857437Lelio R Paula10/2012
91322^190799-11306557437Enzo Doria07/2014
91339*5^82159+257428Lelio R Paula09/2014
9134(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
913515362^5469+5469^1536257422Hans Havermann04/2019
913614005^12586+12586^1400557419Hans Havermann04/2019
9139lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
9138(103*10^57414-1)/357416Serge Batalov12/2014
9137(1654*30^38869-1)/2957416Karsten Bonath05/2017
91402*10^57410+9^5741057411Mike Oakes04/2011
91412^190704-159557408Lelio R Paula05/2011
914211^55121-174057403Enzo Doria11/2012
91432^190644-18557390Lelio R Paula04/2011
914441182!3-3^4118257389Robert Price08/2015
91452^190629-11225557386Enzo Doria06/2014
9146(2*10^57384-71)/357384Robert Price01/2017
91472*6^73735+5^7373557378Mike Oakes11/2009
91482^190605+5957378Lelio R Paula04/2011
91496^73727-757371Lelio R Paula10/2012
91502^190561-11222557365Enzo Doria06/2014
915110^57358+17089957359Patrick De Geest06/2016
915210^57358-800157358Robert Price03/2016
915318^45687-1157350Lelio R Paula02/2013
915411^55069-21057349Enzo Doria07/2012
915511^55068-1257348Lelio R Paula02/2013
915619^44839+5457339Lelio R Paula02/2013
9157(7*2^190468-1)/851157334Lelio R Paula01/2014
9158(23*10^57333-59)/957334Robert Price03/2017
91592^190455-1155*19045557333Henri Lifchitz02/2005
916065^31620+2857325Lelio R Paula01/2016
91612^190403+1609557318Lelio R Paula05/2011
9162(19*10^57316+119)/357317Robert Price02/2017
9165(21*2^190393+1)/21157314Lelio R Paula07/2012
91642^190392-11202557314Enzo Doria05/2014
916313173^13912-13912^1317357314Norbert Schneider08/2018
916614092^11633+11633^1409257294Hans Havermann04/2019
9167(24737*2^190234+1)/957270Lelio R Paula05/2014
9168(7*2^190230+1)/2357265Lelio R Paula07/2012
9169(10223*2^190197+1)/321157256Lelio R Paula05/2014
917016726^2645+2645^1672657244Hans Havermann04/2019
917118^45590-9757228Lelio R Paula02/2013
9172(3*2^190105-1)/1920557224Lelio R Paula01/2014
9173(16*10^57219-31)/357220Robert Price03/2016
9174(2^190074+47)/5157217Lelio R Paula02/2012
91753^119894-14057204Lelio R Paula10/2012
9177(37^36473-1)/3657196Robert Price03/2012
91762^190000-216357196Yves Minet08/2013
91782^189987-279810757192Enzo Doria04/2016
91792^189935-11211757177Enzo Doria05/2014
91802^189909-11223157169Enzo Doria06/2014
9181132049#+14905357161Makoto Morimoto12/2015
918241032!3-2757158Robert Price09/2014
918319^44694+2257153Lelio R Paula02/2013
918412^52956-1757150Lelio R Paula02/2013
91852^189823-96757143Yves Minet01/2012
9186(25*10^57138-61)/957139Robert Price02/2015
91875^81743-4^(81743+1)57136Robert Price04/2016
918814476^8843+8843^1447657131Hans Havermann04/2019
918915327^5338+5338^1532757130Hans Havermann04/2019
91907^67593-5457123Lelio R Paula10/2012
91917*3^119712+257118Lelio R Paula03/2014
91935^81700+1657106Lelio R Paula10/2012
91922^189700+7656157106Enzo Doria05/2016
91952^189671+13157097Lelio R Paula04/2011
91944*6^73374+557097Lelio R Paula09/2014
9196(67607*2^189651+1)/4372757091Lelio R Paula05/2014
9197(29*2^189619-1)/39357080Lelio R Paula01/2014
91983^119587+8057058Lelio R Paula10/2012
91992^189502-11345357046Enzo Doria07/2014
92002^189455+15357032Lelio R Paula04/2011
920124^41317-41317^2457027Norbert Schneider07/2016
92022^189414-1757020Lelio R Paula03/2011
920324^41311+2357018Norbert Schneider12/2013
9204norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
9205(4*10^56989-31)/956989Erik Branger05/2011
920611^54712-162056977Enzo Doria11/2012
92078102^14577-14577^810256976Norbert Schneider01/2019
92082^189237-11223156967Enzo Doria06/2014
920917^46285-4856952Lelio R Paula02/2013
92102^189188+7524156952Enzo Doria04/2016
92112^189181+9439556950Henri Lifchitz01/2005
92127001^14808-10856940Enzo Doria07/2012
92132^189147-11263956939Enzo Doria06/2014
9214(19*10^56933-43)/356934Robert Price10/2017
92152^189110-356928M. Frind & P. Underwood11/2002
92162^189069+1290956916Lelio R Paula04/2011
9217(13*10^56909+191)/356910Robert Price08/2017
9218(35*10^56898-17)/956899Serge Batalov02/2009
92192^189011-595556898Lelio R Paula04/2011
92206^73119-556898Lelio R Paula10/2012
922113^51076-9056896Lelio R Paula02/2013
92222^188997+5689756894Yves Minet02/2010
92235^81388-1376656888Enzo Doria02/2013
9224(104^28201+1)/10556881Richard Fischer04/2018
9225(156^25933+1)/15756873Eric Chen12/2017
922620^43713-640356872Enzo Doria03/2013
9227(71*10^56858-287)/956859Robert Price05/2017
92282^188857-25423356852Gary Barnes09/2009
922915^48338-8856850Lelio R Paula02/2013
923010^56849+13643756850Patrick De Geest07/2017
923110^56849-70156849Robert Price06/2017
9232(2^188788+78557)/356831Lelio R Paula05/2012
92332^188771+1609556826Lelio R Paula04/2011
92347*2^188742-956818Lelio R Paula03/2014
923512^52646-6556815Lelio R Paula02/2013
92365003^15358-15856813Enzo Doria07/2012
92372^188713+57729457556809Lelio R Paula03/2013
923810060^14193-14193^1006056809Norbert Schneider02/2019
92392^188693-11209956803Enzo Doria05/2014
9240(7^67211+4^67211)/1156799Robert Price10/2012
92412^188678-9439556798Lelio R Paula09/2011
924220^43651-850356792Enzo Doria03/2013
92442^188657-237156792Yves Minet10/2013
9243152^26029-151^2602956792Eric Chen04/2018
9245(14^49549+5^49549)/1956789Robert Price05/2013
9246(45^34351-1)/4456788Robert Price05/2014
92477*10^56785-2356786Robert Price04/2016
9248(10^56781-31)/356781Serge Batalov12/2014
92497*10^56779+356780Erik Branger11/2009
9250((10^14197+1)*((10^28394+10^14197)*(10^14197-10^7099+3)-10^7099+2)-1)/3541/340728156778Makoto Kamada03/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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